Weight of suspended bodies; definitions of point, line, surface
Studies on gravity and equilibrium alongside the elements of geometry
On the right Leonardo studies how a rigid ('parallel', i.e. parallelepiped) body suspended between two balances yields different weights at its opposite ends as its inclination and points of contact change, sketching a hanging weight and a quadrant for gauging degrees of obliquity. He states that gravity and levity are contrary accidents that generate one another, that a body reshaped is reweighted, and that every continuous quantity is divisible to infinity. The left face gathers definitions of the geometric primitives — point, line, surface and body — the surface being not part of a body but the common boundary where body meets air. A moralizing aside is addressed to the ambitious who enjoy neither life nor the beauty of the world.
On this page
A suspended rigid body weighs differently at each end
A parallelepiped body suspended between two balances is said to give as many different weights at its opposite ends as there are varieties in the obliquity of its position. Even at a fixed obliquity, the weights vary with the positions of the contacts the supports make with it.
Gravity and levity; smaller surface weighs more; infinite divisibility
Gravity and levity are declared two contrary accidents that generate one another. A body transformed in shape is transformed in weight; the body with the smaller surface weighs more. He closes that every continuous quantity is divisible to infinity.
Definitions of point, line, surface and body
Lines are placed in three positions — level, oblique, perpendicular. A point has no middle and its boundaries are nothing; a line is a length made by the point's motion; a surface is made by the transverse motion of a line; a body's boundaries are surfaces, the surface being the common boundary where body meets air.
A rebuke to the ambitious
Set among the mechanical notes, a moral aside declares that to the ambitious, who are not content with the benefit of life nor with the beauty of the world, it is given as penance that they themselves torment that life and never possess its usefulness and beauty.